The unemployment rate rose to 3.786% from 3.495% on a bigger 736k increase to the size of the labor force than to the employment level, not because people lost jobs.
The employment level actually made a new high in August 2023, but up a smaller 222k.
The unemployment rate went up in August because record new high employment in August, 161.484m, is a smaller percentage of a new larger labor force in August, 167.839m than was the case in July: 96.2% in August vs. 96.5% in July = 3.8% and 3.5% unemployed respectively.
And do not mix the limited Establishment Survey (122,000 businesses and agencies) total nonfarm jobs oranges (156.419m) with the unemployment rate Household Survey (60,000 households) whole universe of jobs apples and try to make them agree. They don't, and never will.
The Establishment Survey went up 187k in August, but the unemployment rate is not derived from that survey.
